4.2.1. The x field of a loaded conductive sphere:
From corollary 4 and equation 4.4 we conclude that the xi electric effects field of an electron belonging to an infinitesimal surface ds of a loaded spherical conductor will be:
 |
|
The meaning of the variables found in equation 4.5 can be obtained from the exam of Figure 7;
Figure 7: Comments in the text
n indicates the number of electrons contained in ds. Under these conditions, the electric effects field in P due to ds will be:
 |
|
and N = 4pRn/ds is the total number of electrons composing the electric charge under consideration.
It elapses from the symmetry of the problem:
|
|
and from equation 4.6:
|
|
With the aid of figure 7 and calling the azimuthal angle j, we can establish the following relationships:
|
|
Substituting 4.9 in 4.8 and simplifying, we have
|
|
Integrating 4.10 [z > r and z < R] and observing 4.7, we have:
Using the conventional notation for distances (r = distance from P to the center of the sphere = z) we finally get to:
|
|
